Random walks on stochastic temporal networks
In the study of dynamical processes on networks, there has been intense focus on network structure—i.e., the arrangement of edges and their associated weights—but the effects of the temporal patterns of edges remains poorly understood. In this chapter, we develop a mathematical framework for random...
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| Format: | Journal article |
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Springer
2013
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| _version_ | 1826342830204780544 |
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| author | Hoffmann, T Porter, M Lambiotte, R |
| author_facet | Hoffmann, T Porter, M Lambiotte, R |
| author_sort | Hoffmann, T |
| collection | OXFORD |
| description | In the study of dynamical processes on networks, there has been intense focus on network structure—i.e., the arrangement of edges and their associated weights—but the effects of the temporal patterns of edges remains poorly understood. In this chapter, we develop a mathematical framework for random walks on temporal networks using an approach that provides a compromise between abstract but unrealistic models and data-driven but non-mathematical approaches. To do this, we introduce a stochastic model for temporal networks in which we summarize the temporal and structural organization of a system using a matrix of waiting-time distributions. We show that random walks on stochastic temporal networks can be described exactly by an integro-differential master equation and derive an analytical expression for its asymptotic steady state. We also discuss how our work might be useful to help build centrality measures for temporal networks. |
| first_indexed | 2024-03-07T02:57:55Z |
| format | Journal article |
| id | oxford-uuid:aff549f8-c928-4892-8963-6f3950e7ff2c |
| institution | University of Oxford |
| last_indexed | 2024-03-07T02:57:55Z |
| publishDate | 2013 |
| publisher | Springer |
| record_format | dspace |
| spelling | oxford-uuid:aff549f8-c928-4892-8963-6f3950e7ff2c2022-03-27T03:52:58ZRandom walks on stochastic temporal networksJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:aff549f8-c928-4892-8963-6f3950e7ff2cSymplectic Elements at OxfordSpringer2013Hoffmann, TPorter, MLambiotte, RIn the study of dynamical processes on networks, there has been intense focus on network structure—i.e., the arrangement of edges and their associated weights—but the effects of the temporal patterns of edges remains poorly understood. In this chapter, we develop a mathematical framework for random walks on temporal networks using an approach that provides a compromise between abstract but unrealistic models and data-driven but non-mathematical approaches. To do this, we introduce a stochastic model for temporal networks in which we summarize the temporal and structural organization of a system using a matrix of waiting-time distributions. We show that random walks on stochastic temporal networks can be described exactly by an integro-differential master equation and derive an analytical expression for its asymptotic steady state. We also discuss how our work might be useful to help build centrality measures for temporal networks. |
| spellingShingle | Hoffmann, T Porter, M Lambiotte, R Random walks on stochastic temporal networks |
| title | Random walks on stochastic temporal networks |
| title_full | Random walks on stochastic temporal networks |
| title_fullStr | Random walks on stochastic temporal networks |
| title_full_unstemmed | Random walks on stochastic temporal networks |
| title_short | Random walks on stochastic temporal networks |
| title_sort | random walks on stochastic temporal networks |
| work_keys_str_mv | AT hoffmannt randomwalksonstochastictemporalnetworks AT porterm randomwalksonstochastictemporalnetworks AT lambiotter randomwalksonstochastictemporalnetworks |